The circular rigid wheel of the HCS-I series Harmonic Drive Reducer is a rigid ring with internal teeth. When the gear of the HCS-I series Harmonic Drive Reducer is assembled, it meshes with the teeth of the Flexspline on the long axis of the wave generator ellipse. This meshing is like an ellipse inscribed in a concentric circle.

Mathematically, an inscribed ellipse will touch a circle at two points. However, the gear teeth of the HCS-I series Harmonic Drive Reducer have a limited height. So there are actually two areas of tooth engagement (instead of two points). Round splines have two more teeth than flex splines and are fixed to the gearbox.
How do the three gear elements mesh and rotate? The diameter of the flexible gear of the HCS-I series Harmonic Drive Reducer is slightly smaller, and the number of teeth is two less than that of the circular rigid gear. The elliptical shape of the wave generator causes the teeth of the flexible gear to mesh with the rigid wheel in two opposing areas on the major axis of the ellipse.
Every time the waveform generator rotates 180 degrees clockwise, the teeth of the flexible wheel of the HCS-I series Harmonic Drive Reducer advance one tooth counterclockwise relative to the rigid wheel. Each clockwise rotation of the Wave Generator causes the Flexspline to move two teeth counterclockwise relative to the Circular Spline from its original position. Harmonic Drive harmonic gears have zero backlashes because the gear teeth are always fully meshed in the area along the main shaft.
Through the above introduction and analysis of the Circular gear for the HCS-I series Harmonic Drive Reducer, hope it helps you.